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# question on buoyancy

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I have read the equations for buoyancy. Basically, the buoyant force is equal to the weight of the water displaced, which is equal to: densitywater * volume water I read that the density of water is 62.4LBs per foot, and in the great salt lake it is closer to 64lbs per foot. My physics books attributes the buoyant force to the fact that the downward pressure is less than the upward pressure, because the downward force acts on the top of a submerged object, which is shallower than the bottom of the submerged object which is simultaneously experiencing a greater upward force because it is deeper. My question is, *how* is there actually an upward force on the bottom of the submerged object? Ive thought about this for a while, and it doesn''t make sense to me at all. Is it just because there''s a ''column'' of water underneath the object, and the ''rest'' of the water is pushing upward almost like water in a straw? Again, I have memorized the equations, but I don''t know why an upward force even exists. Thanks.

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denisty * volume does not equal the force. density * volume * acceleration due to gravity does.

When you submerge an object in a fluid the rest of the fluid around that object raises the exact volume of the displaced fluid (if I haven''t articulated that correctly: when you sit in a bathtub the water level raises).

Gravity pulls all of this fluid downwater but in order for the level of the fluid to reach an equilibrium the column of water under the submerged object is forced upward.

"I forgot I had the Scroll Lock key until a few weeks ago when some asshole program used it. It even used it right" - Conner McCloud

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Also I don''t know why you''d want to use so disgusting units. ~1000 kgm^-3 is a far nicer density I''m sure you''d agree.

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Yes, metric system is soooo much nicer. Especially when it comes to water. And the bouyant force = displaced_volume * density * gravity;

If you don't have the acceleration due to gravity in there your units would cancel out to just mass units (like kg) and you need the acceleration to make it into newtons (kgm/s2

I believe that's an important lesson, always check your units! You're bound to make stupid mistakes if you don't (speaking from experience )

EDIT: And the force comes from the fact that gravity is pushing all the displaced water back down to it's level position, and all that water being pushed down is going to push on the object in the water, and the water under the object is going to push it up, and that's the force you get.

[edited by - Samith on April 20, 2004 5:02:56 PM]

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shadow12345, if you apply pressure to a surface there will be a force acting on the surface. The bigger the pressure, the bigger the force. The water pressure increases with depth, so the pressure acting on the bottom of the submerged object will be bigger than that acting on the top.

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quote:

shadow12345, if you apply pressure to a surface there will be a force acting on the surface. The bigger the pressure, the bigger the force. The water pressure increases with depth, so the pressure acting on the bottom of the submerged object will be bigger than that acting on the top.

Yes, I understand that, I just didn't really *get* why there was even an upward force.

quote:

And the force comes from the fact that gravity is pushing all the displaced water back down to it's level position, and all that water being pushed down is going to push on the object in the water, and the water under the object is going to push it up, and that's the force you get.

Yes, I think that makes the most sense (to me). I *think* that's what i was thinking with the straw analogy I was trying to give, unless I read what you said wrong

quote:

denisty * volume does not equal the force. density * volume * acceleration due to gravity does.

Hmm, I'm confused. A pound is a force, correct? Subsequently saying lbs * volume is the same as saying density * volume * acceleration due to gravity (slugs * volume * 32), unless I missed something?

All in all I think I understand it better, thanks you guys.

EDIT: yeah, metric system is much nicer. I dont' even understand why the english system exists or why it was ever implemented in the first place. Unfortunately, I can only ever seem to remember english system units

[edited by - shadow12345 on April 20, 2004 9:56:40 PM]

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Although this is a homework question, I''ll allow it to remain open since shadow* is actually looking for a deeper understanding of buoyancy. I don''t feel the question he is asking would be asked as a homework or test question at this education level, so I find it to be a legitimate question. Review the Forum FAQ for the general homework policy.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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A pound is a mass and a force. When you are talking density you are talking mass over volume, and then when you mutliply it by volume again you end up with just plain mass. That''s why you multiply again by gravity to get the acceleration (remember F = m*a) then it''s a pound-force. (Sorry I don''t know the correct terminology with the USA system, I was only taught metric.) Hope that helps some.

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quote:
Original post by Samith
it''s a pound-force. (Sorry I don''t know the correct terminology with the USA system, I was only taught metric.)

I dont think most people who use this system know the correct terminology . It''s slugs but I believe foot-pounds is also acceptable.

"I forgot I had the Scroll Lock key until a few weeks ago when some asshole program used it. It even used it right" - Conner McCloud

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quote:
quote:

denisty * volume does not equal the force. density * volume * acceleration due to gravity does.

Hmm, I''m confused. A pound is a force, correct? Subsequently saying lbs * volume is the same as saying density * volume * acceleration due to gravity (slugs * volume * 32), unless I missed something?

A pound, like a kilogram, is a measurement of mass, not force. Weight is a measurement of force (mass*acceleration due to gravity). The difference is that if you go to the moon your mass is the same as when you''re on Earth, but your weight is only one sixth that on Earth.

Scales usually have units in pounds or kilogrammes, but they will only be correct at sea level on the Earth

quote:
EDIT: yeah, metric system is much nicer. I dont'' even understand why the english system exists or why it was ever implemented in the first place.

...or why it''s called the "English" system when we use Systeme Internationale units (metric) over here.

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Forces are in Newton. 1 Newton = 1kg * 1 m/s^2

so, 1 kg of sugar, under normal gravity, will give 9.81 Newton.

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quote:
Original post by Samith
F = m*a) then it''s a pound-force. (Sorry I don''t know the correct terminology with the USA system, I was only taught metric.)

"pound-force"

Hey, you got it right!

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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quote:

Although this is a homework question

Actually no it isn't. I'm on a week long vacation, and I just bought a book called 'Engineering Mathematics' and 'Physics for game developers'. If it was a homework question I would have told you guys.

EDIT:
quote:

"pound-force"

Hey, you got it right!

Okay, I'm really confused. I thought that a pound was the english system equivalent of a newton. Now you are saying that a pound is really mass? I've never heard of that before. I thought a pound was a force, a newton was a force, slugs were mass and kg were also mass. Crap.

EDIT1:
quote:

A pound, like a kilogram, is a measurement of mass, not force

I thought a pound was a measurement of force because it was slugs * acceleration. But now I'm thinking that I'm wrong because I just remembered there's a conversion from pounds to kg, which is 1lb = 2.2kg, which would be impossible if they weren't both the same type of thing.

[edited by - shadow12345 on April 22, 2004 1:12:47 PM]

[edited by - shadow12345 on April 22, 2004 1:18:03 PM]

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Pounds are force, just like newtons. Weight is usually the force due to gravity. Since the acceleration due to gravity is approximately a constant at the earth''s surface, it is possible to convert from pounds to kilograms by calculating the mass needed (in kilograms) to produce the object''s weight at the surface of the earth (in pounds).

Your formula for displacement force, density * volume, is incorrect because that formula only gives the mass of the displaced substance. Assuming that acceleration due to gravity is a constant (which is acceptable at the earth''s surface) allows you to use force per volume * volume, which is what you were actually doing with 62.4 lbs per square foot times the volume.

The reason for the force is this: Pascal''s principle states that in an incompressible and static fluid, each point in the fluid exerts its pressure in all directions equally. The pressure at a point in the fluid increases with depth, because the deeper you go, the more fluid there is above pushing downward. Making a few approximations, we find that the fluid at the top of the object is exerting a downward force and the fluid at the bottom of the object is exerting an upward force on it (there are also forces pushing at the sides of the object, but these all cancel out, since for all the surface area on one side of the object there must be an equal amount of surface area on the other side). The force at the bottom is greater than the force pushing down from the top because the fluid at the bottom is deeper and is under higher pressure. The net force is approximately the mass of the displaced fluid * the acceleration due to gravity (which we are assuming to be a constant, about 9.8 m/s^2 near the earth''s surface).

Perhaps it is easiest to imagine a rectangular object in the water. The top and bottom of the object have a surface area of A, and the distance between the top and bottom sides is D, and the water has density d, and the top of the object is at depth x (too many things start with d...), and acceleration is g. The volume of water above the object pushing down is A * x, so its mass is A*x*d, and the force it is exerting is A*x*d*g. The volume of the water which is above the water which is pushing up on the bottom of the object is A*(x+D), and we get that the total force pushing up is then A*(x+D)*d*g.

From here we find the total upward force is A*(x+D)*d*g - A*x*d*g. Simplifying leads to a net force of A*D*d*g. A*D is the volume of the object, V, so we end up with V*d*g, volume times density times acceleration due to gravity. Now I''m sure there''s some advanced way to prove that this works for arbitrarily shaped bodies, with all the forces cancelling out except for the upward force of V*d*g, but I think this is enough, and you can sort of imagine how the forces cancel out for other shapes.

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I appreciate the lengthy response! I''ve read over several times and I don''t think I have anymore questions

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pounds can be force OR mass. Just make sure you make the distinction in your units. Use lbf or lbm. They are equivalent at sea level on earth.

To convert you need a gravitational constant and acceleration due to gravity. Gc = 32.2 lbm*ft / lbf*s*s

So,
1lbm / 32.2 lbm*ft/lbf*s*s * 32.2ft/s*s = 1lbf
(the units cancel, trust me..its hard to do this on something other than paper)

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CombatWombat,

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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